A projective variety $X$ has canonical singularities if it is normal, if $rK_{X}$ is Cartier for some $r\geq 1$ and if there exists a resolution $f:Y\to X$ such that

$$rK_{Y}=f^{*}(rK_{X})+\sum_{i}a_{i}E_{i},$$

where $E_{i}$ ranges over all exceptional prime divisors of $f$, and $a_{i}\geq 0$.